Abstract
In this paper, we consider the most general treatment of spinor fields, their kinematic classification and the ensuing dynamic polar reduction, for both classes of regular and singular spinors; specifying onto the singular class, we discuss features of the corresponding field equations, taking into special account the sub-classes of Weyl and Majorana spinors; for the latter case, we study the condition of charge-conjugation, presenting a detailed introduction to a newly-defined type of spinor, that is the so-called ELKO spinor: at the end of our investigation, we will assess how all elements will concur to lay the bases for a simple proposal of neutrino mass generation.
Similar content being viewed by others
Change history
12 July 2018
Unfortunately, the original version of this article was published with incorrect ORCID id for the author Luca Fabbri.
References
Abłamowicz, R., Gonçalves, I., Rocha, R.: Bilinear covariants and spinor fields duality in quantum clifford algebras. J. Math. Phys. 55, 103501 (2014)
Ahluwalia, D.V.: The theory of local mass dimension one fermions of spin one half. Adv. Appl. Clifford Algebra 27, 2247 (2017)
Ahluwalia, D.V., Grumiller, D.: Dark matter: a spin one half fermion field with mass dimension one? Phys. Rev. D 72, 067701 (2005)
Ahluwalia, D.V., Grumiller, D.: Spin half fermions with mass dimension one: theory, phenomenology, and dark matter. JCAP 0507, 012 (2005)
Bernardini, A.E.: Chiral oscillations in terms of the zitterbewegung effect. Eur. Phys. J. C 50, 673 (2007)
Bernardini, A.E., Leo, S.D.: Flavor and chiral oscillations with Dirac wave packets. Phys. Rev. D 71, 076008 (2005)
Bernardini, A.E., Rocha, R.: Obtaining the equation of motion for a fermionic particle in a generalized Lorentz-violating system framework. EPL 81, 40010 (2008)
Bernardini, A.E., Rocha, R.: Dynamical dispersion relation for ELKO dark spinor fields. Phys. Lett. B 717, 238 (2012)
Cavalcanti, R.T.: Classification of singular spinor fields and other mass dimension one fermions. Int. J. Mod. Phys. D 23, 1444002 (2014)
Cavalcanti, R.T., Hoff da Silva, J.M., da Rocha, R.: VSR symmetries in the DKP algebra: the interplay between Dirac and Elko spinor fields. Eur. Phys. J. Plus 129, 246 (2014)
Cianci, R., Fabbri, L., Vignolo, S.: Exact solutions for Weyl fermions with gravity. Eur. Phys. J. C 75, 478 (2015)
Cianci, R., Fabbri, L., Vignolo, S.: Critical exact solutions for self-gravitating Dirac fields. Eur. Phys. J. C 76, 595 (2016)
Coronado Villalobos, C.H., Hoff da Silva, J.M., da Rocha, R.: Questing mass dimension 1 spinor fields. Eur. Phys. J. C 75, 266 (2015)
Fabbri, L.: General dynamics of spinors. arXiv:1707.03270
Fabbri, L.: A discussion on the most general torsion-gravity with electrodynamics for Dirac spinor matter fields. Int. J. Geom. Methods. Mod. Phys. 12, 1550099 (2015)
Fabbri, L.: A generally-relativistic gauge classification of the Dirac fields. Int. J. Geom. Meth. Mod. Phys. 13, 1650078 (2016)
Hoff da Silva, J.M., da Rocha, R.: From Dirac action to ELKO action. Int. J. Mod. Phys. A 24, 3227 (2009)
Hoff da Silva, J.M., da Rocha, R.: Unfolding physics from the algebraic classification of spinor fields. Phys. Lett. B 718, 1519 (2013)
Lounesto, P.: Clifford Algebras and Spinors. Cambridge University Press, Cambridge (2001)
da Rocha, R., Cavalcanti, R.T.: Flag-dipole and flagpole spinor fluid flows in Kerr spacetimes. Phys. Atom. Nucl. 80, 329 (2017)
da Rocha, R., Hoff da Silva, J.M.: From Dirac spinor fields to ELKO. J. Math. Phys. 48, 123517 (2007)
da Rocha, R., Hoff da Silva, J.M.: ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration. Adv. Appl. Clifford Algebra 20, 847 (2010)
da Rocha, R., Pereira, J.G.: The Quadratic spinor Lagrangian, axial torsion current, and generalizations. Int. J. Mod. Phys. D 16, 1653 (2007)
da Rocha, R., Bernardini, A.E., Hoff da Silva, J.M.: Exotic dark spinor fields. JHEP 1104, 110 (2011)
da Rocha, R., Fabbri, L., Hoff da Silva, J.M., Cavalcanti, R.T., Silva-Neto, J.A.: Flag-dipole spinor fields in ESK gravities. J. Math. Phys. 54, 102505 (2013)
Rodrigues, W.A., Rocha, R., Vaz, J.: Hidden consequence of active local Lorentz invariance. Int. J. Geom. Meth. Mod. Phys. 2, 305 (2005)
Vaz Jr., J.: The Clifford algebra of physical space and Dirac theory. Eur. J. Phys. 37, 055407 (2016)
Vignolo, S., Fabbri, L., Cianci, R.: Dirac spinors in Bianchi-I f(R)-cosmology with torsion. J. Math. Phys. 52, 112502 (2011)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Jayme Vaz
Rights and permissions
About this article
Cite this article
Fabbri, L. Spinor Fields, Singular Structures, Charge Conjugation, ELKO and Neutrino Masses. Adv. Appl. Clifford Algebras 28, 7 (2018). https://doi.org/10.1007/s00006-018-0821-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00006-018-0821-7